Graphing and Magnitude of a Complex Number
Read this topicExplanations 4
- The Magnitude of a Complex Number Earlier, we related complex numbers to vectors on the complex plane. We saw how adding complex numbers is essentially equivalent to adding vect…
By Eric Zhang, Expii Team
- Magnitude of Complex Numbers The magnitude of a complex number is its distance from the origin in the complex plane. The concept may seem a little bit foreign right now as you b…
By Jonathan Heller, Caroline K, Victor Wang, Anusha Rahman
- (Video) The Magnitude of a Complex Number by James Hilburn In this video by James Hilburn, you can see an example of how to find the magnitude of a complex number by graphing. S…
By Anusha Rahman
- Graphing a Complex Number and Finding the Magnitude In our previous lessons, we learned the basics of complex numbers and how to multiply them. In this lesson, we’re going to di…
By Anusha Rahman
Problems 22
- What is the magnitude of 5+12i5 + 12i5+12i?
- Find the magnitude of the complex number 4−3i4-3i4−3i.
- What is the magnitude of the complex number 1−i1-i1−i?
- A modulus of a number is the distance from the origin to the number's point on a graph. We use ∣z∣|z|∣z∣ to denote the modulus of zzz. To figure out the modulus we use the equat…
- Let z=x+iy.z=x+iy.z=x+iy. Solve for y:y:y: ∣z∣<∣z+i∣|z|<|z+i|∣z∣<∣z+i∣
- Let z=x+iy.z=x+iy.z=x+iy. Solve for y:y:y: ∣3z∣<∣2i−3z∣|3z|<|2i-3z|∣3z∣<∣2i−3z∣
- What is the magnitude of 3+4i3+4i3+4i?
- What is the magnitude of 5+2i5+2i5+2i?
- Let z,wz,wz,w be complex numbers with magnitudes ∣z∣=1|z| = 1∣z∣=1 and ∣w∣=4|w| = 4∣w∣=4. What is the largest possible value of the magnitude ∣z−w∣?|z-w|?∣z−w∣?
- Let z,wz,wz,w be complex numbers with magnitudes ∣z∣=1|z| = 1∣z∣=1 and ∣w∣=4|w| = 4∣w∣=4. What is the largest possible value of ∣(3+4i)z−w∣|(3+4i)z-w|∣(3+4i)z−w∣?
- What is the smallest possible value of ∣(2+3i)−(a+bi)(1+i)∣|(2+3i) - (a+bi)(1+i)|∣(2+3i)−(a+bi)(1+i)∣ for integers a,ba,ba,b?
- How many points z=a+biz = a+biz=a+bi in the complex plane, with a,ba,ba,b integers, satisfy ∣z∣=1?|z| = 1?∣z∣=1?
- Let zzz be a complex number of magnitude 101010. What is ∣2z‾∣?|2\overline{z}|?∣2z∣?
- What is the value of the sum ∑z1∣1−z∣2,\sum_z \frac{1}{{\left|1 - z\right|}^2} ,z∑∣1−z∣21, where zzz ranges over all 7 solutions (real and nonreal) of the equation z7=−1z^7 = …
- Let z=3eπ6i+2e5π3iz = 3e^{\frac{\pi}{6}i} + 2e^{\frac{5\pi}{3}i}z=3e6πi+2e35πi. What is ∣z∣2|z|^2∣z∣2?
- In the complex plane, the number line has two axes: one real, one imaginary. The real line is as normal, and the imaginary line is exactly like the real line, except vertical di…
- Let aaa and bbb be complex numbers. If ∣a∣=5|a| = 5∣a∣=5 and ∣b∣=7|b| = 7∣b∣=7, what is the value of ∣a‾⋅b‾∣?|\overline{a}\cdot \overline{b}|?∣a⋅b∣?
- Consider the set of complex numbers z=a+biz = a+biz=a+bi with magnitude ∣z∣=5|z|=5∣z∣=5, such that aaa and bbb are integers. How many pairs of complex conjugates are in this set?
- How many complex numbers with integer real and imaginary parts have a magnitude of 111, 222, 333, 444, or 555?
- For a complex number z=a+biz=a+biz=a+bi, determine: ∣z+z‾∣\lvert z+\overline{z}\rvert∣z+z∣
- For a complex number z=a+biz=a+biz=a+bi, determine: ∣z−z‾∣\mid z-\overline{z}\mid∣z−z∣
- For a complex number z=a+biz=a+biz=a+bi, determine: ∣zz‾∣\mid z\overline{z}\mid∣zz∣